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Green's function for tangentialy loaded horizontaly layered half-space
Tomaž Pliberšek, Andrej Umek, 2008, original scientific article

Abstract: The topic of this paper is a novel evaluation of the integral representation of the surface Greenćs function for a layered half-space, loaded on its surface by a harmonic tangential point force. The equations of motions are reduced to wave equations by the introduction of wave potentials. The Hankel transform is applied to them and they are consecutively solved leading to the integral representation of surface displacements. They are consecutively evaluated by the proposed three step procedure. First the singularity is extracted. It is further noted that so obtained integrals, after suitably chosen branch cuts and analytic continuation of integrands are introduced, can be evaluated by contour integration for an arbitrary number of layers. They are, therefore, expressed by number of residues at the poles of integrand and the integrals along finite portions of the branch cuts. The latter ones can easily be evaluated to any desired accuracy leading to a closed form solution. Some numerical results corroborating the presented approach are given.
Keywords: elastodynamics, elastic wave propagation, Green`s function, horizontaly layered half-space, horizontal point load
Published in DKUM: 05.06.2018; Views: 1106; Downloads: 79
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Evaluation of Green`s function for vertical point-load excitation applied to the surface of a semi-infinite elastic medium
Andrej Štrukelj, Tomaž Pliberšek, Andrej Umek, 2006, original scientific article

Abstract: The topic of this paper is to show that the integrals of infinite extent representing the surface displacements of a layered half-space loaded by a harmonic, vertical point load can be reduced to integrals with finite integration range. The displacements are first expressed through wave potentials and the Hankel integral transform in the radial coordinate is applied to the governing equations and boundary conditions, leading to the solutions in the transformed domain. After the application of the inverse Hankel transform it is shown that the inversion integrands are symmetric/antimetric in the transformation parameter and that this characteristic is preserved for any number of layers. Based on this fact the infinite inversion integrals are reduced to integrals with finite range by choosing the suitable representation of the Bessel function and use of the fundamental rules of contour integration, permitting simpler analytical or numerical evaluation. A numerical example is presented and the results are compared to those obtained by the CLASSI program.
Keywords: civil engineering, soil mechanics, Green`s function, layered half-space, vertical point load
Published in DKUM: 31.05.2012; Views: 2227; Downloads: 39
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